Lorentz transformations (time dilation)

[Ascendant78]

Homework Statement

A rocket ship carrying passengers blasts off to go from
New York to Los Angeles, a distance of about 5000 km.
(a) How fast must the rocket ship go to have its own
length shortened by 1%? (b) Ignore effects of general
relativity and determine how much time the rocket
ship’s clock and the ground-based clocks differ when
the rocket ship arrives in Los Angeles.

Homework Equations

Since I solved for (a) and got the correct answer (0.14c or approx. 4.2x10⁷m/s), here is the equation for (b) that I used:

T' = T_o/(sqrt(1-β²)

alternate formula:

t'₂ - t'₁ = ((t₂ - t₁) - (v/c^2)(x₂ - x₁)/(sqrt(1-β^2)

The Attempt at a Solution

Total travel time = 0.119s (5E6/4.2E7)
Velocity = 4.2E7

So:

T' = 0.119/(sqrt(1-4.2E7^2/3E8^2))
This gave me 1.2E-1s (or about 120ms)

alternately (second formula):

T' = (0.119 - (4.2E7/c^2)(5E6)/(sqrt(1-(4.2E7^2/c^2)))
This gave me 1.17E-1s (or about 120ms)

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It seems like both are giving me the same answer, but are off by a factor of 100 (since both round to 120ms and the correct answer is 1.2ms). Can someone please let me know where I'm going wrong?

 

[vela]

You've calculated the time elapsed on the two clocks, but the question is asking for the difference between the two clocks.

 

[Ascendant78]

You've calculated the time elapsed on the two clocks, but the question is asking for the difference between the two clocks.

Oh wow, I can't believe I overlooked that fact. Thank you.